<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Examples</title>
<link rel="stylesheet" href="../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Math Toolkit 3.3.0">
<link rel="up" href="../cstdfloat.html" title="Chapter 3. Specified-width floating-point typedefs">
<link rel="prev" href="macros.html" title="Floating-Point Constant Macros">
<link rel="next" href="float128_hints.html" title="Hints on using float128 (and __float128)">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
<td align="center"><a href="../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="macros.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../cstdfloat.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="float128_hints.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.examples"></a><a class="link" href="examples.html" title="Examples">Examples</a>
</h2></div></div></div>
<h4>
<a name="math_toolkit.examples.h0"></a>
      <span class="phrase"><a name="math_toolkit.examples.je_lambda"></a></span><a class="link" href="examples.html#math_toolkit.examples.je_lambda">Jahnke-Emden-Lambda
      function</a>
    </h4>
<p>
      The following code uses <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">cstdfloat</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
      in combination with <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code> to
      compute a simplified version of the <a href="http://mathworld.wolfram.com/LambdaFunction.html" target="_top">Jahnke-Emden-Lambda
      function</a>. Here, we specify a floating-point type with <span class="bold"><strong>exactly
      64 bits</strong></span> (i.e., <code class="computeroutput"><span class="identifier">float64_t</span></code>).
      If we were to use, for instance, built-in <code class="computeroutput"><span class="keyword">double</span></code>,
      then there would be no guarantee that the code would behave identically on
      all platforms. With <code class="computeroutput"><span class="identifier">float64_t</span></code>
      from <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">cstdfloat</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>,
      however, it is very likely to be identical.
    </p>
<p>
      Using <code class="computeroutput"><span class="identifier">float64_t</span></code>, we know that
      this code is as portable as possible and uses a floating-point type with approximately
      15 decimal digits of precision, regardless of the compiler or version or operating
      system.
    </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">cstdfloat</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// For float_64_t, float128_t. Must be first include!</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">cmath</span><span class="special">&gt;</span>  <span class="comment">// for pow function.</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// For gamma function.</span>
</pre>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">jahnke_emden_lambda</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">x</span><span class="special">)</span>
<span class="special">{</span>
  <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">gamma_v_plus_one</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">v</span> <span class="special">+</span> <span class="number">1</span><span class="special">);</span>
  <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">x_half_pow_v</span>     <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">(</span><span class="identifier">x</span> <span class="special">/</span><span class="number">2</span><span class="special">,</span> <span class="identifier">v</span><span class="special">);</span>

  <span class="keyword">return</span> <span class="identifier">gamma_v_plus_one</span> <span class="special">*</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">v</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">x_half_pow_v</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
      Ensure that all possibly significant digits (17) including trailing zeros are
      shown.
    </p>
<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span><span class="special">&gt;::</span><span class="identifier">max_digits10</span><span class="special">);</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">setf</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios</span><span class="special">::</span><span class="identifier">showpoint</span><span class="special">);</span> <span class="comment">// Show trailing zeros.</span>

<span class="keyword">try</span>
<span class="special">{</span> <span class="comment">// Always use try'n'catch blocks to ensure any error messages are displayed.</span>

<span class="comment">// Evaluate and display an evaluation of the Jahnke-Emden lambda function:</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">v</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">jahnke_emden_lambda</span><span class="special">(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 0.88010117148986700</span>
</pre>
<p>
      For details, see <a href="../../../example/cstdfloat_example.cpp" target="_top">cstdfloat_example.cpp</a>
      - a extensive example program.
    </p>
<h4>
<a name="math_toolkit.examples.h1"></a>
      <span class="phrase"><a name="math_toolkit.examples.normal_table"></a></span><a class="link" href="examples.html#math_toolkit.examples.normal_table">Normal
      distribution table</a>
    </h4>
<p>
      This example shows printing tables of a normal distribution's PDF and CDF,
      using <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span></code> implementation of normal distribution.
    </p>
<p>
      A function templated on floating-point type prints a table for a range of standard
      variate z values.
    </p>
<p>
      The example shows use of the specified-width typedefs to either use a specific
      width, or to use the maximum available on the platform, perhaps a high as 128-bit.
    </p>
<p>
      The number of digits displayed is controlled by the precision of the type,
      so there are no spurious insignificant decimal digits:
    </p>
<pre class="programlisting"><span class="identifier">float_32_t</span>    <span class="number">0</span>    <span class="number">0.39894228</span>
<span class="identifier">float_128_t</span>  <span class="number">0</span>    <span class="number">0.398942280401432702863218082711682655</span>
</pre>
<p>
      Some sample output for two different platforms is appended to the code at
      <a href="../../../example/normal_tables.cpp" target="_top">normal_tables.cpp</a>.
    </p>
<pre class="programlisting"><span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_FLOAT32_C</span>
    <span class="identifier">normal_table</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float32_t</span><span class="special">&gt;();</span> <span class="comment">// Usually type float</span>
<span class="preprocessor">#endif</span>
    <span class="identifier">normal_table</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span><span class="special">&gt;();</span> <span class="comment">// Usually type double. Assume that float64_t is always available.</span>
<span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_FLOAT80_C</span>
    <span class="identifier">normal_table</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float80_t</span><span class="special">&gt;();</span> <span class="comment">// Type long double on some X86 platforms.</span>
<span class="preprocessor">#endif</span>
<span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_FLOAT128_C</span>
    <span class="identifier">normal_table</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float128_t</span><span class="special">&gt;();</span> <span class="comment">// Type _Quad on some Intel and __float128 on some GCC platforms.</span>
<span class="preprocessor">#endif</span>
    <span class="identifier">normal_table</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">&gt;();</span>
</pre>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
      Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
      Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
      Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
      Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="macros.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../cstdfloat.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="float128_hints.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>
